The Digital Transmission Range sensor (DTR) controls current flow when 'R' is selected for the back up lamps.. Be sure to check fuse position 5, 15amp fuse.. Here is a pic of the DTR.. It mounts to the side of the trans where the shift cable/arm connect..

What engine do you have, and whats the build date of the truck? I can give you the connector configuration/wire colors to check/probe for DTR function for the back up lights to verify/diagnose the switch prior to replacement..